## How do I solve a set of equations in Maple?...

Hi,

I want to solve a set of ODE(s) by Maple. How do I do that?(Please, see the attached file)
Thanks.

new.mw

## Non-linear Equations...

Hi,

I have three equations in terms of the following variables:

X,Y,X1, X2

How do I get an equation in terms of (X1,X2)  with Maple from Equations 1-3?

E.mw

Hi,

s1.mw

## How do I show animated point on odeplot?...

`restart;`

`with(plots);`

`a:=0.2; b:=0.2; c:=5.7;`

`ode1:=diff(x(t),t)=-y(t)-z(t);`

`ode2:=diff(y(t),t)=x(t)+a*y(t);`

`ode3:=diff(z(t),t)=b+z(t)*(x(t)-c);`

`ic1:=x(0)=-0.7;`

`ic2:=y(0)=-0.7;`

`ic3:=z(0)=1;`

`sol:=dsolve({ode1,ode2,ode3,ic1,ic2,ic3},{x(t),y(t),z(t)},numeric,method=classical[rk4],stepsize=0.10,output=listprocedure);`
`b:=rhs(sol[2]);`

`c:=rhs(sol[3]);`

`d:=rhs(sol[4]);`

```animate (pointplot3d, [ [b(t),c(t),d(t)], symbol=box, color=blue],t=15..100, background = odeplot(sol, [x(t),y(t),z(t)],t=15..100,numpoints=7000),frames=20);```

UPD
And "Error, (in plots/animate) incorrect first argument" BUT if i use classic functions (sin,cos,sqrt) instead of b,c,d - all is well.

For example [sin(t),cos(t),t/10]

For example [b(t),c(t),d(t)]
Error, (in plots/animate) incorrect first argument

## How to plot an equation?...

Hi,
I want to plot an equation, but I couldn't. Who can guide me?

Ra.mw

## Solve an equation...

Hi,

I want to solve an equation(see the attached file) numerically, find  values of M that satisfy this equation and then plot the curve of M versus sigmai for those values of M that satisfy the mentioned equation. How can I do that with Maple?

eq.mw

## How do I solve a set of equations numerically in M...

Hi,

How do I solve numerically this set of equations with the following ICs to plot U1(x), phi(x),diff(phi(x),x) versus x:

diff(U1(x),x)=-diff(phi(x),x)/(U1(x)-T/U1(x));
diff(phi(x),x\$2)=(1+A1*phi(x)+A2*phi(x)**(3/2)+A3*phi(x)**2)-(M1/U1(x));
where

A1:=(2*k-1)/(2*k-3);
A2:=8*sqrt(2/pi)*(beta-1)*k*Gamma(k)/(3*Gamma(k-0.5)*(2*k-3)**(3/2));
A3:=(4*k**2-1)/(2*(2*k-3)**2);
M1=0.1+sqrt(T+(1/A1));
(Gamma is gamma function)

assume, for example, T=0.1, pi=3.14, beta=0.6, k=3.5

ICs:

U1(x=0)=M1, phi(x=0)=0, diff(phi(x=0),x)=0.001.

Thanks.

## Planar dynamical system...

Hi,

Consider the following planar dynamical system(PDS) with parameters r, p1, s, n:
a:=(r+1)*(1+p1*s)/(2*(1-P1))-1/(n^2);
b:=(r+1)*(3-r)*(1-p1*s^2)/(8*(1-p1))-3/(2*n^4);
c:=(r+1)*(3-r)*(5-3*r)*(1+p1*s^3)/(48*(1-p1))-5/(2*n^6);

## Contour plot with Maple...

Hi,

I need to plot a contour plots of x versus f that satisfy two following equations

2.884460657-2.884460657*sqrt(1-.6933705250*x)-5.000000000*f*(1-(1-.8*x)^.2500000000)-(12.50000000*(1-f))*(1-(1-.32*x)^.2500000000) = 0;

1/sqrt(1-.6933705250*x)+1.250000000*f/(1-.8*x)^.7500000000+(3.125000000*(1-f))/(1-.32*x)^.7500000000 = 0

How can I do that by Maple?

If the coefficient of x can be changed from 0.1 to 0.6, what is your suggestion(s) to  repeat the above process for each of these coefficients?

## Finding the intersection point...

Hellow everyone,

Consider the following diffrential equation:

(dA(x)/dx )^2+V(A)=0,
1- How to plot dA/dx vs A?

2- How to find the coordinate of intersection point of f(x)=e-b*exp(x)-c*(1-2*x/c)^(1/2) with df/dx? e,b,c are constants.

## how to do that?...

Considering the follwoing expr:

A(x):=mue+(mun/gama)+(u0^2)-mud*x-mue*exp(x)-(mun/gama)*exp(gama*x)-(u0^2)*(1-2*x/u0^2)^(1/2);

where

mue:=1/(1+alpha+beta);
mun:=alpha/(1+alpha+beta);
mud:=beta/(1+alpha+beta);
u0:=(mue+mun*gama)^(-1/2);
and assuming the values of alpha and beta lie between 0.1..0.6 and gama=15 ro 20.

How do I determine those values of (alpha,beta,gama) satisfying conditions [(3), (4)], [(3), (5)] or [(3),(6)]?

conditions:

A(x[m] <> 0) = 0:

where x_m is an extreme point of A(x) (other than x=0),

d*A(x)/dx, x = x[m] < 0:

d*A(x)/dx, x = x[m] > 0:

d*A(x)/dx, x = x[m] = 0:

## Simplifying a polynomial!...

Hi,
How do I simplify the following polynomial:

-(729 beta (1/2 (-1/9 (-5/27 beta-1/9) lambda^6-1/9 (1/9 beta^2 TT+(10/9 TE+2/3 TT) beta-1/9 TE) lambda^4+5/27 (2/5 TT (3/2 TT+TE) beta+TE (TE-2/5 TT)) beta lambda^2-1/9 TE beta^2 TT (-TT+TE)) p1(m,t)^2+(beta TT-1/3 lambda^2)^2 (-1/3 lambda^2+TE)^3 ((p2(m,t))/(lambda^2-3 TE)+3/2 ((lambda^2+TE) p1(m,t)^2)/((lambda^2-3 TE)^3))))/((3 beta TT-lambda^2)^3 (3 TE-lambda^2)^2),

as follows:

-3*beta*p2(m,t)/(lambda^2-3*beta*TT)+3*beta^2*(5*lambda^2-3*beta*TT)*p1(m,t)^2/(2*(lambda^2-3*beta*TT)^3)
?

## How to solve system of PDEs?...

I want to solve the following system of PDEs with Maple:

In fact, I want to determine q1,n1,p1,nn1,qn1,pn1 as a functions of pphi1 (assume  ne1(X,T)=(alpha/(2))*pphi1(X,T))

(mu, nu, beta, lambda, TE , alpha and TT are constant, but q1,n1,p1,nn1,qn1,pn1 depend on (X,T))

How do I do that?

> diff(q1(X, T), X)-lambda*(diff(n1(X, T), X)) = 0;

diff(pphi1(X, T), X)+TE*(diff(p1(X, T), X))-lambda*(diff(q1(X, T), X)) = 0;

-lambda*(diff(p1(X, T), X))+3*(diff(q1(X, T), X)) = 0;

-lambda*(diff(nn1(X, T), X))+diff(qn1(X, T), X) = 0;

-lambda*(diff(qn1(X, T), X))+beta*TT*(diff(pn1(X, T), X))-beta*(diff(pphi1(X, T), X)) = 0;

-lambda*(diff(pn1(X, T), X))+3*(diff(qn1(X, T), X)) = 0;

-mu*ne1(X, T)-nu*nn1(X, T)+n1(X, T) = 0;

## How to change coordinate?...

How can I transform the following differential equation from (x,t) to (X,T) coordinate, where, for example, X=x-alpha*t, T=beta*t (alpha and beta are constant)

diff(z, t)+(diff(R, x))*L+A*(diff(L, x))+diff(k, x, x)-(diff(k, t, t)) = 0

Thanks.

## How do I solve my Eqs. in Maple?...

Suppose two following Eqs.:

(1) du/dt+d(u*w)/dx=0

(2) dw/dt+wdw/dx=0

I want to expand u(x,t) and w(x,t) in the power series of epsilon

u=u0+epsilon*u1+epsilon^2*u2+…

w=w0+epsilon*w1+epsilon^2*w2+…

and change the variables x,t to X,T as follows

X=(x-alpha*t) and T=beta*t,

and solving Eqs. (1) and (2) for different order of epsilon (epsilon, epsilon^2, epsilon^3,…) to finding u0,w0,u1,w1,…

How do I do that?

Thanks.

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